⚡ Physics Excellence Test ⚡

The SI unit of electric charge is:

Two point charges +Q and -Q are placed at a distance d apart. The electric field at the midpoint between them is:

The electric field inside a hollow conducting sphere is:

The dimension of electric potential is:

When a dielectric slab is inserted between the plates of a charged capacitor, the capacitance:

The work done in moving a charge on an equipotential surface is:

The value of permittivity of free space (ε₀) is approximately:

Two capacitors of capacitance C₁ and C₂ are connected in series. The equivalent capacitance is:

Electric field lines are:

The energy stored in a capacitor is given by:

Define electric dipole moment.

What is the relation between electric field and electric potential?

State the principle of quantization of charge.

State and explain Gauss's theorem in electrostatics.

Derive the expression for the electric field due to an electric dipole at a point on its equatorial line.

Explain the concept of dielectric constant and dielectric strength.

What are equipotential surfaces? State their properties.

Using Gauss's law, derive the expression for electric field intensity due to an infinitely long straight uniformly charged wire.

Derive an expression for the capacitance of a parallel plate capacitor. How does it change when a dielectric slab is introduced between the plates?

Explain the energy stored in a capacitor. Derive the expression for energy density in an electric field.

State and prove the principle of superposition of electric charges. Give two applications.

(a) State Coulomb's law and express it in vector form.
(b) Three charges +2q, -q, and +3q are placed at the vertices of an equilateral triangle of side 'a'. Calculate the electric potential at the centroid of the triangle.

(a) Using Gauss's law, derive an expression for the electric field due to a uniformly charged infinite plane sheet.
(b) Two large parallel conducting plates are placed close to each other with a small separation. The inner faces carry surface charge densities +σ and -σ. Find the electric field in the regions (i) between the plates (ii) outside the plates.

(a) Derive an expression for the electric field intensity at a point on the axial line of an electric dipole.
(b) An electric dipole of length 2 cm is placed with its axis making an angle of 60° with a uniform electric field of 10⁵ N/C. If it experiences a torque of 8√3 Nm, calculate the magnitude of charge on the dipole.

(a) Explain the combination of capacitors in series and parallel. Derive expressions for equivalent capacitance in both cases.
(b) Three capacitors of 2 μF, 3 μF, and 6 μF are connected first in series and then in parallel. Find the ratio of equivalent capacitances in the two cases.

(a) Derive an expression for the energy stored in a charged capacitor.
(b) A parallel plate capacitor with air as dielectric has a capacitance of 10 μF. When a dielectric slab is introduced between the plates, the capacitance becomes 50 μF. The capacitor is charged to 100 V and then the battery is disconnected. Calculate: (i) the charge on the capacitor (ii) the energy stored before and after introducing the dielectric.

Case Study: Electric field lines provide a visual representation of the electric field in a region of space. They have specific properties that help us understand the nature of electric fields.

Based on this information, answer the following:
(a) Why do electric field lines never intersect?
(b) What does the density of field lines indicate?
(c) Draw electric field lines for: (i) a positive point charge (ii) two equal positive charges (iii) a dipole.

Two point charges +8 μC and -8 μC are placed at a distance of 20 cm apart.
(a) Calculate the electric field intensity at the midpoint of the line joining them.
(b) Find the point on the line where electric potential is zero.
(c) Calculate the electric potential at a point 15 cm from each charge.
(Take k = 9 × 10⁹ Nm²/C²)

A parallel plate capacitor has plates of area 0.04 m² separated by a distance of 2 mm. A dielectric slab of thickness 1 mm and dielectric constant 5 is introduced between the plates.
(a) Calculate the capacitance before introducing the dielectric.
(b) Calculate the capacitance after introducing the dielectric.
(c) If a potential difference of 100 V is applied, find the charge stored and energy stored in both cases.
(ε₀ = 8.85 × 10⁻¹² C²/Nm²)

In a circuit, four capacitors of capacitances C₁ = 4 μF, C₂ = 6 μF, C₃ = 12 μF, and C₄ = 3 μF are connected. C₁ and C₂ are in series, their combination is in parallel with C₃, and the whole assembly is in series with C₄. A 120 V battery is connected across the combination.
(a) Draw the circuit diagram.
(b) Calculate the equivalent capacitance.
(c) Find the charge on C₄ and the potential difference across C₃.
(d) Calculate the total energy stored in the system.